抽象群概念由法国天才数学家伽罗华（Eacute;variste Galois，1811-1832）最先建立起来。群的定义有多种等价的表达形式，以这一种最为基本。
然而，即使对于本原群，其次轨道的决定也是一个非常困难的问题，它依赖与人们对抽象群本身结构的了解和一些组合方法的应用。
However, such a problem is very difficult in general, even for primitive groups and it depends heavily on the understanding of abstract groups and the application of combinatorial tools as well.
我觉得在我的职业生涯中，最大的变化在于人们不再把神经系统简单地当做一群抽象的子系统来研究，却对行为不管不问。
I think the major change that has occurred during my career is the fact that people no longer study the nervous system simply as a set of abstract subsystems, without recourse to behavior.
这些对象的结构性能进行了研究的群，环，域和其他抽象的系统，其本身这样的对象的研究。
The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects.
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